Fused Lasso approach in portfolio selection

In this work we present a new model based on a fused Lasso approach for the multi-period portfolio selection problem in a Markowitz framework. In a multi-period setting, the investment period is partitioned into sub-periods, delimited by the rebalancing dates at which decisions are taken. The model leads to a constrained optimization problem. Two l1penalty terms are introduced into the objective function to reduce the costs of the investment strategy. The former is applied to portfolio weights, encouraging sparse solutions. The latter is a penalization on the difference of wealth allocated across the assets between rebalancing dates, thus it preserves the pattern of active positions with the effect of limiting the number of transactions. We solve the problem by means of the Split Bregman iteration. We show results of numerical tests performed on real data to validate our model.